Given a list of strings, what is the longest substring common to all of them?

Input

The first line of input contains an integer $n$ ($1 \le n \le 1\,000$), which is the number of strings that follow.

Each of the next $n$ lines contains a single string $s$ ($1 \le |s| \le 100$) consisting only of lower-case letters.

Output

Output a single integer, which is the length of the longest substring common to all of the input strings.

Examples

Input 1

5
axabcrwmvd
abcn
tabchwqsl
bvrkabcayna
tyabc

Output 1

3